I then tried changing all the cells to DIVs and positioning everything using CSS, but floating logo left and user info right made them hang down past the banner+navigation.
Floating divs are a good approach!
I'll give you a very useful tip:
HTML Code:
<div style="float: left; width: 200px; height: 100px; background: yellow;"></div>
<p>This is a paragraph of text.</p>
This will show the div next to the text. (Try it!)
HTML Code:
<div style="float: left; width: 200px; height: 100px; background: yellow;"></div>
<div style="clear: both;"></div>
<p>This is a paragraph of text.</p>
This will show the floated div and the text starts below it.